I just finished reading that article, and I do have a few questions about it:
First of all, why does it have to be either a cube or a hexagonal prism? Why not a dodecahedron or an isocahedron in which the opposite faces are glued together? That would allow for rotations of 72 or 144 degrees for the dodecahedron and 120 for the isocahedron. For that matter, why not a tetrahedron, the simplest of shapes, or a sphere in which every pair of opposite points are glued together, or a cylinder with the same properties for the sides of it as the sphere, and with the two ends simply glued together, or glued together with a certain rotation (and with any possible rotation, since they are circles.) Also, with the cubes, why is it that only one pair of faces could be glued together with a certain rotation? Why not two, or all of the pairs of faces? With that situation in there with two cubes on top of one-another, why could we not add more cubes and make it even more complicated?

Also, why are we automatically assuming that we will be able to see ourselves through one of those glued-together sides? After all, on earth, you cannot get a good telescope and look in one direction and see the back of your own head, and neither could you see the entire surface of the earth from any vantage point; an ant on a torus would not be able to see itself, or even the entire torus from any position. How do we know that the curvature of the universe into 5th+ dimensions that causes this shape to arise doesn't also limit our perception of it, in the same way that the curvature of the earth into the third dimension limits our perception of its surface?